Rinse the squid and pat dry. Slice tubes into ½-inch rings; leave tentacles whole or cut into smaller clusters.
Bring a pot of water to a rolling boil with 1 teaspoon salt and 1 teaspoon rice vinegar.
Drop in the squid and boil for 90 seconds to 2 minutes, until opaque and just curled at the edges.
Immediately transfer the squid to an ice bath using a slotted spoon. Let it cool for 1–2 minutes, then drain well.
Drain the sansai mix through a fine mesh strainer and pat dry with paper towels.
In a small bowl, whisk together the soy sauce, rice vinegar, sugar, mirin, toasted sesame oil, and ginger until the sugar dissolves.
Combine the drained squid and sansai mix in a large bowl. Pour over the dressing and toss gently to coat.
Chill for at least 15 minutes before serving.
Garnish with sliced scallion and toasted sesame seeds just before serving.